With the rack in the middle position, preheat the oven to 425°F (220°C).
Place the squash halves in a large baking dish, cut side up. Brush with 1 tbsp (15 ml) of the oil. Season with salt and pepper. Cover with aluminum foil and bake for 45 minutes. Remove the foil. Place the onion wedges around the squash, drizzle with 1 tbsp (15 ml) of the oil and continue baking for 30 minutes.
In a skillet over medium-high heat, lightly brown the garlic in the remaining oil. Add the arugula and cook for 1 minute.
Arrange the squash and onions on a serving platter. Top with the arugula and sprinkle with the cheese. Delicious with onion soup-roasted turkey (see recipe).